Let's say I am reviewing galley proofs, and the author has written some text in italics which shouldn't be. Would I write: “please typeset this word in roman” or “please typeset this word upright”? If both are clear and understandable, what are the differences?

I don't know if there's an answer that's standard in the industry (hence why this is a comment not an answer), but personally I'd go for upright since Roman is ambiguous (it can either mean not-italic or not-sans-serif.
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psmearsMar 12 '11 at 17:06

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I'm in the industry. We use the term "roman" to mean "not-italics." Curiously, it is almost always used in cases where something is in italics and you need to undo it. It is common to say things like, "that needs to be in italics," but you pretty much never have occasion to say, "this text needs to be in roman." Rather, it's when something is in italics and it shouldn't be that the term "roman" comes into play.
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The RavenMar 12 '11 at 21:29

In my case, it's most often because people typeset text as part of math expressions (like subscripts) that end up italicized (math style) when they should be in roman.
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F'xMar 12 '11 at 21:31

3 Answers
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Once again I turn to The Chicago Manual of Style, 14th Edition, which states

2.83: [...] To change words typeset in an italic typeface, underline or circle the words and write "rom" or "roman" in the margin. For longer underlined passages that are to be set in roman type (not italicized), circle the text involved and write a note to the typesetter in the margin:
(set roman) [parentheses here indicates that text is circled]

Speaking as someone who has done a little bit of proofreading work, using the word "roman" (in lowercase) in this context will not be confusing to anyone on the receiving end of the proofing notes.

In typography terminology, roman (or normal) is the antonym of italic, while upright is the antonym of oblique (aka slanted). Oblique type and italic type are not the same, as the Wikepedia article 'Oblique type' explains and illustrates. Some typefaces have separate italic and oblique fonts. No typeface (AFAIK) has separate roman and upright fonts, so the choice between these words depends on which of italic or upright you wish to draw a contrast with. So if the author has inappropriately used an italic font rather than a slanted font, 'please typeset in roman' would strictly be more appropriate than 'please typeset upright'. But the typesetter will set the same type whichever you use.

Regarding the oppositions roman/italic and upright/oblique, it would totally make my day! It would be clear and convenient. However, language isn't always so convenient, so I have to ask: can you quote any reference to back it up?
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F'xMar 12 '11 at 22:41